SOLUTION: A grocer prepares a mixture of 20 lb. of dried apples and pears to sell for $2.95 per pound. Dried apples cost $2.20 per lb. and dry pears cost $3.20 per lb. How much of each type

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Question 1103699: A grocer prepares a mixture of 20 lb. of dried apples and pears to sell for $2.95 per pound. Dried apples cost $2.20 per lb. and dry pears cost $3.20 per lb. How much of each type must the grocer use?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52794)   (Show Source):
You can put this solution on YOUR website!
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Let "a" be the amount of dried apples (in pounds) and "p" be the amount of dried pears. a + p = 20 (1) (dried appples + dried pears = 20 pounds) 2.20*a + 3.20*p = 2.95*20 (2) (cost + cost = cost in dollars) Multiply eq(1) by 2.20 (both sides). The modified system is 2.20*a + 2.20*p = 2.20*20, (1') 2.20*a + 3.20*p = 2.95*20. (2') Now subtract eq(1') from eq(2'). The terms "2.20*a" will cancel each other, and you will get a single equation for only ONE unknown "p". (It is how the Elimination method works) You will get 3.20p - 2.20p = 2.95*20 - 2.20*20 ====> p = 0.75*20 = 15. Answer. 15 pounds of dried pears and 20-15 = 5 pounds of dried apples. Check. 2.20*5 + 3.20*15 = 59 dollars. 2.95*20 = 59 dollars. ! Correct !

Solved.

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There is entire bunch of lessons covering various types of mixture problems
    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Word problems on mixtures for antifreeze solutions
    - Word problems on mixtures for dry substances like coffee beans, nuts, cashew and peanuts
    - Word problems on mixtures for dry substances like candies, dried fruits
    - Word problems on mixtures for dry substances like soil and sand
    - Word problems on mixtures for alloys
    - Typical word problems on mixtures from the archive
    - Advanced mixture problems
    - Advanced mixture problem for three alloys
    - OVERVIEW of lessons on word problems for mixtures
in this site.

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Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

If you understand to use it, the method of alligation will get you to the answer to most "mixture" problems much faster than the traditional algebraic solution shown by most tutors.

Here is how to solve this particular mixture problem using the method of alligation.

The numbers in the third column give the ratio in which the dried apples and dried pears should be mixed. Since that ratio is .25:.75, or 1:3, you need 5 pounds of dried apples and 15 pounds of dried pears to make 20 pounds of the mixture.

Here is an explanation of how this method works...

The first row of this diagram is for the dried apples, which cost 2.20 per pound; the last row is for the dried pears, which cost 3.20 per pound. The middle row is for the mixture, which is to cost 2.95 per pound.

The numbers in the third column are the differences, computed diagonally, between the numbers in the first and second columns: 3.20-2.95 = .25; 2.95-2.20=.75.

Those numbers in the third column, calculated in that way, show the ratio in which the dried apples and dried pears need to be mixed.

In this problem, that ratio is .25:.75, or 1:3. That means 1/4 of the mixture must be dried apples and 3/4 must be dried pears.

Since the mixture is to be 20 pounds, you need 5 pounds of dried apples and 15 pounds of dried pears.